'We're starting to turn the corner,' the mayor of New Orleans says. But suffering and bitterness remain in the chaotic, ruined city.

NEW ORLEANS — An influx of National Guard troops speeded evacuation efforts and brought a relative calm to this devastated city Saturday, but authorities continued to struggle to evacuate thousands, to quell sporadic fires and looting, and to cope with a diaspora of the dispossessed fanning out across the nation.

President Bush ordered 7,200 Army and Marine reinforcements to join a National Guard force expected to swell to 40,000 regionally in coming days. The military helped clear the squalid Superdome shelter and vastly reduced the encampment at the city's convention center, nearly a week after massive flooding unleashed by Hurricane Katrina.

"I don't know if the cavalry has arrived, but there is definitely progress being made," said New Orleans Mayor C. Ray Nagin. "We're starting to turn the corner."

While much of the city remained underwater, the landmark French Quarter and Garden District stood mostly dry Saturday, as did much of Uptown to the north and west of downtown. Like the rest of the city, those areas remained without power and drinking water.

Addressing the nation from the White House on Saturday, Bush reiterated his acknowledgment a day earlier that the relief effort had initially fallen short, but he said added forces would help set New Orleans and Mississippi's Gulf Coast in order.

"Hour by hour, the situation on the ground is improving," Bush said. "Yet the enormity of the task requires more resources and more troops."

The pledges continued to sound hollow to many of those awaiting relief in 95-degree heat and stifling humidity, including Larry Martin, 35, who had been waiting four days to be bused from the convention center.

"They embraced and they cried on Sept. 11; they cried for the tsunami," Martin said.

"But they just left us here to die.... We survived the hurricane, and now we're still fighting to survive a week later. It's crazy."

Stepped-up federal efforts were matched by what charities said were record donations by the public -- totaling more than $400 million -- and Internet campaigns that had thousands of Americans offering to house the dispossessed.

Under fierce criticism from flood victims and regional political leaders, Bush and his emergency management team sought to emphasize progress made. But they also conceded that recovery would be enormous work.

By Saturday, an estimated 51,480 of the homeless had been placed in 127 Red Cross shelters in Louisiana and another 220,000 in hotels and shelters in Texas.

Local and federal authorities opened two jails to hold suspected looters and others thought to be preying on the vulnerable. And officials had begun to plan how to collect and catalog the dead, opening the first temporary morgue.

"We're taking the streets back from criminals who have attempted to terrorize citizens," said the U.S. attorney for the region, Jim Letten.

Still, New Orleans officials estimated at least several thousand people remained stranded in the city. They received at least 1,000 calls from people pleading to be rescued from attics, porches and rooftops.

The Army Corps of Engineers estimated it would need at least 36 days to pump water out of the city and as much as 80 days to drain the water from neighboring parishes.

Other challenges loomed. Crews worked to repair 881,730 phone lines and to restore power to 668,000 Louisiana homes that survived the storm.

Complaints about the speed and tactics of the relief efforts persisted Saturday, with Louisiana's two Democratic senators saying the federal government should already have offered direct cash aid to flood victims.

And one state senator from Baton Rouge -- frustrated at seeing thousands of evacuees waiting to be taken from a camp on Interstate 10 -- hired three Greyhound buses to ship families to an Air Force base in the center of the state.

Sen. Cleo Fields said the evacuees would be delivered to England Air Force Base in central Louisiana and that he would demand that they be housed and fed.

Although much of the focus remained on helping the stranded, authorities began to turn more attention to the dead.

An inkling of the grim work ahead emerged Saturday: Emergency crews arriving in Chalmette, just south of New Orleans, learned that 31 residents in a nursing home had died when floodwaters filled the facility, and rescuers found the bodies of 21 others from the fishing and oil community roped together.

"I want the world to know that federal and state help did not show up here right away," said Fire Chief Tommy Stone. "Let me tell you, if they can't come help us now, God help us if there is ever a terrorist attack."

The relentless stress of the unfolding tragedy spared no one, including the rescuers. A distraught police officer shot himself to death Friday night at a staging area in Algiers, across the Mississippi River from New Orleans.

Mayor Nagin said that several thousand firefighters and police would soon need relief: "They are really starting to show some signs of cracking."